Another possibility to generate the header is to use tikz with the options of remember picture, overlay,transform shape, which basically overlaps a tikz-generated header on top of the page. At the end of this message, I put the code to do that. What I am doing:
- I changed the top margin to 2.5 cm via the
geometry package to leave space for the header.
- I generated the header using
tikz and multiline nodes, since it allows for centering of the text without having to guess its position via hspace.
- I place the different nodes approximately 1cm above the text body and the line between them via the
calc library.
Do note that all of this positioning is manual. If you change the value for the top margin in the declaration of the geometry package, you will need to adjust the different sizes manually.
The text does not overlap the header because the header has been placed above the text body (!) which removes the problem that you had before. Other possibility to achieve a similar effect without having to change how to generate the header can be enveloping your header in a minipage environment with a set height, but I am not sure if this will work.
I hope it helps you!
The result is the following:

And the code to achieve this:
\documentclass[journal, a4paper, 11pt]{IEEEtran}
\IEEEoverridecommandlockouts
\linespread{1.25}\selectfont
\usepackage{graphicx}
\usepackage{tabularx}
\usepackage{multirow}
\usepackage{multicol}
\usepackage[table,xcdraw]{xcolor}
\usepackage{tabulary}
\usepackage{url}
\usepackage{amsmath}
\usepackage[left=1.5cm,right=1.5cm,top=2.5cm,bottom=1.5cm]{geometry} %<- Here I changed the top value to make space for the header!
\usepackage{float}
\usepackage{tikz} % Extra!
\usepackage{tikzpagenodes} % To employ the command "current page text area" for positioning of tikz nodes
\usetikzlibrary{calc} % To help with positioning
\usepackage{lipsum} % To generate fake text
%\usepackage{showframe} % To show page geometry
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% ENCABEZADO DE LAS PÁGINAS TIPO UNICAFAM %%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\MYhead}{%
\scriptsize
\hfil\parbox[t][\height][t]{\textwidth}{%
\centering
\begin{picture}(0,0) \put(-30,-27){%
\includegraphics[width=17mm]{example-image-a}}%
\end{picture}%
\hfill PRÁCTICA DE CIRCUITOS I \hfill Versión 1.0 - Page \thepage\
\hfill DEPARTAMENTO DE INGENIERÍA DE TELECOMUNICACIONES \hfill Periodo 2022-II\
\underline{\hspace{\textwidth}}}\hfil\hbox{}}
\newcommand{\tikZHeader}{%
% Useful links:
% For relative positioning: https://tex.stackexchange.com/questions/89588/positioning-relative-to-page-in-tikz
% Ikz and overlay: https://tex.stackexchange.com/questions/121393/tikz-header-and-footer-across-top-and-bottom-of-bulletin-newsletter-page
% Calc library: https://tex.stackexchange.com/questions/617027/how-to-add-a-few-points-to-the-current-page-text-area-of-tikz
% Maybe the header is better with the fancyheader package? : https://www.overleaf.com/learn/latex/Headers_and_footers
\begin{tikzpicture}[remember picture, overlay,transform shape]
%- Node with university logo (left side) -%
\node (leftText) [anchor = south west, inner sep=0pt] % Anchors are tricky!
at ($(current page text area.north west) - (0cm,-1cm)$) % Put the node at the upper left (north west) side of the body of text. Then add 1 cm towards the top of the page, so it is separated from the text.
{%
\includegraphics[width=17mm]{example-image-a}%
};
%- Node with text on center of page -%
\node (centerText) [anchor = south, inner sep=0pt, style={align=center, font = \scriptsize}]
at ($(current page text area.north) - (0cm,-1cm)$) % Put the node at the upper center (north) side of the body of text. Then add 1 cm towards the top of the page, so it is separated from the text.
{%
PRÁCTICA DE CIRCUITOS I \ DEPARTAMENTO DE INGENIERÍA DE TELECOMUNICACIONES \ Periodo 2022-II
};
%- Node with text on right side -%
\node (rightText) [anchor = south east, inner sep=0pt, style={align=right, font = \scriptsize}]
at ($(current page text area.north east) - (0cm,-1cm)$) % Put the node at the upper right (north east) side of the body of text. Then add 1 cm towards the top of the page, so it is separated from the text.
{%
Versión 1.0 - Page \thepage
};
%- Line below header -%
\draw ($(current page text area.north west) - (0cm,-0.5cm)$) -- ($(current page text area.north east) - (0cm,-0.5cm)$) ;
\end{tikzpicture}
}
\makeatletter
% normal pages
\def\ps@headings{%
\def@oddhead{\tikZHeader}%
\def@evenhead{\tikZHeader}}%
% title page
\def\ps@IEEEtitlepagestyle{%
\def@oddhead{\tikZHeader}%
\def@evenhead{\tikZHeader}}%
\makeatother
% make changes take effect
\pagestyle{headings}
% adjust as needed
\addtolength{\footskip}{0\baselineskip}
\addtolength{\textheight}{-10\baselineskip}
\pagenumbering{Roman}
\begin{document}
% Titulo
\title{ \vspace*{15mm} \textbf{\huge{This is the title}} \
\vspace{5mm}
\large{Group Design Project} \
\vspace{5mm}
\large{\textbf{Astronautics and Space Engineering MSc.}} \
\vspace{3mm}
\normalsize{Academic year: 2022-2023}
}
% author names
\author{\textbf{\textbf{Yi Qiang Ji Zhang}}\textsuperscript{1} \ \vspace{3mm}
\textbf{Supervisors}: Dr. s\textsuperscript{1} & Dr. s\textsuperscript{1} \ \vspace{3mm}
\begin{figure}[H]
\centering
\includegraphics[width=0.2\textwidth]{example-image-b}
\hspace{3mm}
\includegraphics[width=0.2\textwidth]{example-image-c}
\end{figure}
\begin{flushleft}
\small{\textsuperscript{1}\textit{School of Aerospace, Transport and Manufacturing, Cranfield University, United Kingdom}}
\end{flushleft}
}% <-this % stops a space
\onecolumn
\maketitle
\newpage
\lipsum[10-25] % fake text
\end{document}