There are two approaches that I can think of. The first is to define a custom style that's modified to check for the user1 field. For example:
\documentclass{article}
\usepackage{lmodern}
\usepackage[utf8]{inputenc}
\usepackage[acronym, nomain, nonumberlist, toc]{glossaries-extra}
\setabbreviationstyle[acronym]{long-short-user}
\makeglossaries
\newacronym[user1=Signal to Noise Ratio]{snr}{SNR}{relación señal a ruido}
\newacronym{utn}{UTN}{Universidad Tecnológica Nacional}
\newglossarystyle{bilinguallist}{%
\setglossarystyle{list}% base it on the list style
\renewcommand*{\glossentry}[2]{%
\item[\glsentryitem{##1}%
\glstarget{##1}{\glossentryname{##1}}]
\ifglshasfield{\glsxtruserfield}{##1}%
{\textit{\glscurrentfieldvalue} (\glossentrydesc{##1})}%
{\glossentrydesc{##1}}%
\glspostdescription\space ##2}%
}
\setglossarystyle{bilinguallist}% set this new style
\begin{document}
Primer uso de \gls{snr}. Segundo uso de \gls{snr}.
Primer uso de \gls{utn}. Segundo uso de \gls{utn}.
\printglossaries
\end{document}

The second method modifies \glossentrydesc which is used in all the predefined glossary styles when displaying the description.
With the base glossaries package, this command just checks if the entry has been defined and displays the description. The glossaries-extra package redefines this command to set the current abbreviation style and check for the attributes glossdescfont and glossdesc before displaying the description.
If you're not interested in using the glossdescfont and glossdesc attributes, you could just redefine \glossentrydesc like this:
\documentclass{article}
\usepackage{lmodern}
\usepackage[utf8]{inputenc}
\usepackage[acronym, nomain, nonumberlist, toc]{glossaries-extra}
\setabbreviationstyle[acronym]{long-short-user}
\makeglossaries
\newacronym[user1=Signal to Noise Ratio]{snr}{SNR}{relación señal a ruido}
\newacronym{utn}{UTN}{Universidad Tecnológica Nacional}
\renewcommand{\glossentrydesc}[1]{%
\glsdoifexistsorwarn{#1}%
{%
\glssetabbrvfmt{\glscategory{#1}}%
\ifglshasfield{\glsxtruserfield}{#1}%
{\textit{\glscurrentfieldvalue} (\glsentrydesc{#1})}%
{\glsentrydesc{#1}}%
}%
}
\begin{document}
Primer uso de \gls{snr}. Segundo uso de \gls{snr}.
Primer uso de \gls{utn}. Segundo uso de \gls{utn}.
\printglossaries
\end{document}
The result is the same as before.
\setglossarystyle{long}. Thank you. – Matías Leonel Martini Aug 17 '17 at 14:17