The command \glsgenacfmt
determines what exactly is printed when you typeset an acronym with \gls
and friends. It uses the \glsentryshort
(and the uppercase and plural forms) when the acronym has already been used.
We can redefine \glsgenacfmt
and replace all instances of entryshort
with entrylong
. Then we get:

\documentclass{article}
\usepackage[nonumberlist]{glossaries}
\renewcommand*{\glsgenacfmt}{%
\ifdefempty\glscustomtext{%
\ifglsused\glslabel{%
\glsifplural{%
\glscapscase
{\acronymfont{\glsentrylongpl{\glslabel}}\glsinsert}%
{\acronymfont{\Glsentrylongpl{\glslabel}}\glsinsert}%
{%
\mfirstucMakeUppercase
{\acronymfont{\glsentrylongpl{\glslabel}}\glsinsert}%
}%
}%
{%
\glscapscase
{\acronymfont{\glsentrylong{\glslabel}}\glsinsert}%
{\acronymfont{\Glsentrylong{\glslabel}}\glsinsert}%
{%
\mfirstucMakeUppercase
{\acronymfont{\glsentrylong{\glslabel}}\glsinsert}%
}%
}%
}%
{%
\glsifplural{%
\glscapscase
{\genplacrfullformat{\glslabel}{\glsinsert}}%
{\Genplacrfullformat{\glslabel}{\glsinsert}}%
{%
\mfirstucMakeUppercase
{\genplacrfullformat{\glslabel}{\glsinsert}}%
}%
}%
{%
\glscapscase
{\genacrfullformat{\glslabel}{\glsinsert}}%
{\Genacrfullformat{\glslabel}{\glsinsert}}%
{%
\mfirstucMakeUppercase
{\genacrfullformat{\glslabel}{\glsinsert}}%
}%
}%
}%
}%
{\glscustomtext}%
}
\setacronymstyle{long-short}
\newacronym[longplural={acronyms},shortplural={ACRs}]{REF}{ACR}{acronym}
\makeglossaries
\begin{document}
First use: \Gls{REF} \par
2nd and following use: \Gls{REF} and \gls{REF}
\printglossaries
\end{document}
Disclaimer: I am not terribly familiar with glossaries
and I do hope there is an easier way, but I haven't found one. (That doesn't mean there isn't one, of course.)