Keen to have gym in the basement (5)
I believe the answer is:
crypt
'basement' is the definition.
(thesaurus)
'keen to have gym' is the wordplay.
'keen' becomes 'cry' (I've seen this in other clues).
'to have' is a charade indicator (letters next to each other).
'gym' becomes 'pt'.
'cry'+'pt'='CRYPT'
'in the' is the link.
(Other definitions for crypt that I've seen before include "Vault beneath a church" , "Underground cell" , "Underground chapel" , "Cellar in church" , "Underground room of church" .)