I can't resit to make some refinements to nice CarLaTeX answer:

Diferences in MWE are indicated by % <-- ...:
\documentclass[12pt,a4paper,twoside]{report}
\usepackage{amsmath, amssymb}
\usepackage{makecell}% <-- added
\usepackage{tikz}
\usetikzlibrary{arrows, calc, positioning, tikzmark}
\usepackage[showframe]{geometry}
\begin{document}
\begin{table}
\setcellgapes{5pt}% <-- added
\makegapedcells % <-- added
\small
\setlength\tabcolsep{4pt}
% \bgroup % <-- its purpose is not clear, so I delete it
\begin{tabular}{|*{3}{>{$\displaystyle}c<{$}|}}% <-- changed
\hline
\mu \in Y
& \text{Condition applied on }\delta(\mu) & \text{Implication upon lifting} \\ \hline
-4 & \left(\frac{13\cdot1789}{q}=-1\right) & n \not\equiv k-4 \pmod{2k} \\ \hline
-3 & \left(\frac{5\cdot29}{q}=-1\right) & n \not\equiv k-3 \pmod{2k} \\ \hline
-2 & \vphantom{\frac{A}{B}} - % <-- added
& - \tikzmark{here} \\ \hline
-1 & \left(\frac{5\cdot29}{q}=-1\right) & n \not\equiv k-1 \pmod{2k} \\ \hline
0 & \left(\frac{13\cdot1789}{q}=-1\right) & n \not\equiv k \pmod{2k} \\ \hline
3 & \left(\frac{5333\cdot97324757}{q}=-1\right) & n \not\equiv k+3 \pmod{2k} \\ \hline
\end{tabular}
% \egroup
\caption{Conditions following from pushing up modulus.}
\label{condition}
\end{table}
\begin{tikzpicture}[overlay,remember picture,node distance=20mm]
\node[right=of pic cs:here] (a) {$\rightarrow$};
\node[draw, rounded corners, align=left, right=0mm of a] {%
Refer Theorem \dots \\ in Section \dots \\ of Chapter 5 };
\end{tikzpicture}
\end{document}
Addendum:
Similarly can be improved answer of Jan. With use of tabularx environment the forth column newer protrude right text margin. With \parbox the content of row is vertically centered:
\documentclass[12pt,a4paper,twoside]{report}
\usepackage{amsmath, amssymb}
\usepackage{makecell, tabularx}% <-- added
\usepackage{array}
\usepackage[showframe]{geometry}
\begin{document}
\begin{table}
\setcellgapes{5pt}% <-- added
\makegapedcells % <-- added
\setlength\tabcolsep{4pt}% <-- changed
\small
\begin{tabularx}{\textwidth}{|*{3}{>{$\displaystyle}c<{$}|}X}% <-- changed
\cline{1-3}
\mu \in Y
& \text{Condition applied on }\delta(\mu) & \text{Implication upon lifting} \\\cline{1-3}
& \text{Condition applied on }\delta(\mu) & \text{Implication upon lifting} \\\cline{1-3} \cline{1-3}
-4 & \left(\frac{13\cdot1789}{q}=-1\right) & n \not\equiv k-4 \pmod{2k} \\\cline{1-3}
-3 & \left(\frac{5\cdot29}{q}=-1\right) & n \not\equiv k-3 \pmod{2k} \\\cline{1-3}
-2 & - & - & \parbox{\linewidth}{\raggedright% <-- added
$\rightarrow$ refer Theorem $x$ in Section $y$ of chapter 5} \\\cline{1-3}
-1 & \left(\frac{5\cdot29}{q}=-1\right) & n \not\equiv k-1 \pmod{2k} \\\cline{1-3}
0 & \left(\frac{13\cdot1789}{q}=-1\right) & n \not\equiv k \pmod{2k} \\\cline{1-3}
3 & \left(\frac{5333\cdot97324757}{q}=-1\right) & n \not\equiv k+3 \pmod{2k} \\\cline{1-3}
\cline{1-3}
\end{tabularx}
\end{table}
\end{document}
which gives:

Addendum (2):
Alternatively can be improved Jan's answer with use of cellspace. Using it the column type X from tabularx package can be redefined as:
\renewcommand\tabularxcolumn[1]{m{#1}}%
what with makecell due to incompatibility between macros \makegapedcells and m{...} column type is not possible. With this change a \parbox used in addendum, is not needed anymore.
Use of cellspace require extension of column types with S, i,e. instead of c had to be used Sc:
\documentclass[12pt,a4paper,twoside]{report}
\usepackage{amsmath, amssymb}
\usepackage{cellspace, tabularx}% <-- added
\renewcommand\tabularxcolumn[1]{m{#1}}% <-- added
\usepackage{array}
\usepackage[showframe]{geometry}
\begin{document}
\begin{table}
\setlength\cellspacetoplimit{5pt} % <-- added
\setlength\cellspacebottomlimit{5pt} % <-- added
\setlength\tabcolsep{4pt}% <-- changed
\small
\begin{tabularx}{\textwidth}{|*{3}{>{$\displaystyle}Sc<{$}|}
>{\raggedright\arraybackslash} X}% <-- changed
\cline{1-3}
\mu \in Y
& \text{Condition applied on }\delta(\mu) & \text{Implication upon lifting} \\\cline{1-3}
& \text{Condition applied on }\delta(\mu) & \text{Implication upon lifting} \\\cline{1-3} \cline{1-3}
-4 & \left(\frac{13\cdot1789}{q}=-1\right) & n \not\equiv k-4 \pmod{2k} \\\cline{1-3}
-3 & \left(\frac{5\cdot29}{q}=-1\right) & n \not\equiv k-3 \pmod{2k} \\\cline{1-3}
-2 & - & - & $\rightarrow$ refer Theorem $x$ in Section $y$ of chapter 5 \\\cline{1-3}
-1 & \left(\frac{5\cdot29}{q}=-1\right) & n \not\equiv k-1 \pmod{2k} \\\cline{1-3}
0 & \left(\frac{13\cdot1789}{q}=-1\right) & n \not\equiv k \pmod{2k} \\\cline{1-3}
3 & \left(\frac{5333\cdot97324757}{q}=-1\right) & n \not\equiv k+3 \pmod{2k} \\\cline{1-3}
\cline{1-3}
\end{tabularx}
\end{table}
\end{document}
Obtained result is the same as before.
\marginpar? – Jan Dec 25 '16 at 08:06\input{preamble.tex}. BTW you don't have to sepcify.texin that case. Your MWE will compile, if you add\usepackage{amsmath}instead. – Jan Dec 25 '16 at 08:07\bgroup/\egroupis not necessary, see Torbjørn T.'s answer here: http://tex.stackexchange.com/a/345639/101651. – CarLaTeX Dec 25 '16 at 20:42