So there are two things going on here: 1. IEEEtran
redefines the standard LaTeX description
environment which acro
defaults to using, 2. You are unsuccessful in trying to apply the tabularray
list template.
To fix the default acro
list we can
either redefine the description
environment or modify the
acro
list template to use a different
environment.
As IEEEtran
makes the standard LaTeX description
environment available as LaTeXdescription
the latter is probably best.
We can redefine the acro
list description template using
\RenewAcroTemplate[list]{description}{% \acroheading
\acropreamble \begin{LaTeXdescription}
\acronymsmapF{%
\item[\acrowrite{short}\acroifT{alt}{/\acrowrite{alt}}]
\acrowrite{list}%
\acroifanyT{foreign,extra}{ (}%
\acroifT{foreign}{\acrowrite{foreign}\acroifT{extra}{, }}%
\acroifT{extra}{\acrowrite{extra}}%
\acroifanyT{foreign,extra}{)}%
\acropagefill
\acropages
{\acrotranslate{page}\nobreakspace}
{\acrotranslate{pages}\nobreakspace}%
}
{\item\AcroRerun} \end{LaTeXdescription} }
or to avoid hard-coding the template we can patch it locally when using \printacronyms
\begingroup
\let\description\LaTeXdescription
\let\enddescription\endLaTeXdescription
\printacronyms
\endgroup

Instead to use the tabularray
list template, we need to do a few
things. acro
no longer uses package
options to set things like this, preferring \acsetup
instead,
although I'm not sure that template=tabularray
has ever been a
valid package option to acro
.
You should be getting a package warning
Package acro Warning: Unknown option `template'
(acro) I don't know the option `template'. Please make sure
(acro) there is no typo. Check the manual for help.
Checking Section 5 Setting options of the
acro
manual we see
\acsetup{<options>}
is preferred. \acsetup{template=tabularray}
yields an error so going to Section 11 Printing the list we see it's
\acsetup{list/template=tabularray}
. This yields another error
! Package acro Error: The template `tabularray' needs the package `tabularray'
(acro) loaded on line 21
which is straightforward, loading the
tabularray
package the new
list template is active and compiles successfully.

The following code is compilable for either solution, just comment out \acsetup{list/template=tabularray}
to get the default description version.
\documentclass[10pt,journal]{IEEEtran}
\usepackage{lipsum}
\usepackage{tabularray}
\usepackage{acro}
\acsetup{list/template=tabularray}
\RenewAcroTemplate[list]{description}{%
\acroheading
\acropreamble
\begin{LaTeXdescription}
\acronymsmapF{%
\item[\acrowrite{short}\acroifT{alt}{/\acrowrite{alt}}]
\acrowrite{list}%
\acroifanyT{foreign,extra}{ (}%
\acroifT{foreign}{\acrowrite{foreign}\acroifT{extra}{, }}%
\acroifT{extra}{\acrowrite{extra}}%
\acroifanyT{foreign,extra}{)}%
\acropagefill
\acropages
{\acrotranslate{page}\nobreakspace}
{\acrotranslate{pages}\nobreakspace}%
}
{\item\AcroRerun}
\end{LaTeXdescription}
}
\DeclareAcronym{a}{
short=aaa,
long=aaaaa,
}
\DeclareAcronym{b}{
short=bbbbbbbb,
long=bbbbbbb bbbbbbb bbbbbbb,
}
\begin{document}
\section*{Nomenclature}
\printacronyms
\section{Introduction}
\lipsum[1]
\ac{a} \ac{b}
\lipsum[1]
\end{document}