Old lady with it, starting to enjoy rock (7)
I believe the answer is:
granite
'rock' is the definition.
(granite is a kind of rock)
'old lady with it starting to enjoy' is the wordplay.
'old lady' becomes 'gran' (I've seen this before).
'with' means one lot of letters go next to another.
'starting to' suggests taking the first letters.
The initial letter of 'enjoy' is 'e'.
'gran'+'it'+'e'='GRANITE'
(Other definitions for granite that I've seen before include "Tangier (anag.)" , "Coarse-grained igneous rock" , "Very hard type of rock" , "Crystalline rock" , "Constituent in Dartmoor" .)