You've indicated in a comment that you use Times (New) Roman as your text font. Most Times Roman-like fonts do not provide a "swashy" ampersand character, but the newtx
font package does. :-) The following MWE shows both the italic and "normal" form of the character that's produced by this font family:

\documentclass{article}
\usepackage{newtxtext,newtxmath}
\begin{document}
\textit{\&} vs.\ \&
\end{document}
Addendum If the character shown above is not "swashy" enough for your taste you could try a font such as Palatino
or Caslon
. (The screenshot you provided in your posting would seem to come from the font Adobe Caslon Pro
.) Note that some of the swashy ampersands employ a fancy combination of an uppercase E
and a lowercase t
, whereas others consist of an equally fancy combination of a lowercase e
and a lowercase t
.

% !TEX TS-program = lualatex
\documentclass{article}
\usepackage{fontspec}
\begin{document}
\setmainfont{Latin Modern Roman} \textit{\&}
\setmainfont{Palatino nova} \textit{\&}
\setmainfont{TeX Gyre Pagella} \textit{\&} % a Palatino clone
\setmainfont{Adobe Caslon Pro} \textit{\&}
\setmainfont{EB Garamond} \textit{\&}
\setmainfont{Garamond Premier Pro} \textit{\&}
\setmainfont{ITC Galliard Std} \textit{\&}
\setmainfont{Junicode} \textit{\&}
\end{document}
(To compile the preceding MWE use either XeLaTeX or LuaLaTeX; pdfLaTeX won't work. Of course, you'll also have to have the various fonts installed on your system.)
And, if you have access to Zapfino
you can choose from seven [7!] different variants of &
:
% !TEX TS-program = xelatex
\documentclass{article}
\usepackage{fontspec}
\setmainfont{Zapfino}
\begin{document}
\addfontfeature{Variant=1} \&
\addfontfeature{Variant=2} \&
\addfontfeature{Variant=3} \&
\addfontfeature{Variant=4} \&
\addfontfeature{Variant=5} \&
\addfontfeature{Variant=6} \&
\addfontfeature{Variant=7} \&
\end{document}

\textit{\&}
?{\usefont{OT1}{cmtt}{m}{it} \&}
or{\usefont{OT1}{cmr}{m}{it} \&}
.