Here's an approach that avoids the scary (?{ code })
and (??{ code }) regex constructs, but whether it's more
readable than your while loop is another question.
>perl -wMstrict -le
"my $s = '_+0GAA__+1GAA__+2GGAA__+3GGGAA_';
print qq{'$s'};
$s =~ s{ ( \+ (\d+) [ACGT]+ ) }
{ (my $r = $1) =~ s{ \+ \d+ [ACGT]{$2} }{}xms; $r }xmsge;
print qq{'$s'};
"
'_+0GAA__+1GAA__+2GGAA__+3GGGAA_'
'_GAA__AA__AA__AA_'
Note that the '+0ACGT' sequence is handled in a way
that seems consistent with your original regex, but that I
don't know to be correct.
Update: Here's a version using substr that might be a
bit more readable.
>perl -wMstrict -le
"my $s = '_+0GAA__+1GAA__+2GGAA__+3GGGAA_';
print qq{'$s'};
$s =~ s{ ( \+ (\d+) [ACGT]+ ) }
{ substr $1, 1 + length($2) + $2 }xmsge;
print qq{'$s'};
"
'_+0GAA__+1GAA__+2GGAA__+3GGGAA_'
'_GAA__AA__AA__AA_'