I found this processing is very difficult for me. Almost I gave up. Did somebody wite such an AppleScript?
input: {“a”,{“b”,“c”}}
output: {“a_1”,{“b_1”,“c_1”}}
I gave up to use recursive call 
This script works for limited condition data.
set aaList to {“1”, {“2”, “3”, “4”}}
set aRes to procList(aaList) of me
→ {“1_new”, {“2_new”, “3_new”, “4_new”}}
on procList(aList)
set outList to {}
repeat with i in aList
set aClass to class of i
if aClass = list then
set aTmp to {}
repeat with ii in i
set tmpTmp to (ii as string) & "_new"
set the end of aTmp to tmpTmp
end repeat
else
set aTmp to (i as string) & "_new"
end if
set the end of outList to aTmp
end repeat
return outList
end procList
No, this is not a recursive subprogram. Here is the real recursive approach (the number of nested elements levels is unlimited):
set aaList to {"1", {"2", "3", "4"}}
set aaList to recursive_procedure(aaList)
on recursive_procedure(theList)
repeat with i from 1 to (count of theList)
set theItem to item i of theList
if class of theItem = list then
my recursive_procedure(theItem)
else
set item i of theList to (theItem & "_new")
end if
end repeat
return theList
end recursive_procedure
Oh! Your code seems 65535 times better than my code! Thank!