Creamy centre of pecorino eaten by climber (5)
I believe the answer is:
ivory
'creamy' is the definition.
(I've seen this before)
'centre of pecorino eaten by climber' is the wordplay.
'centre of' means to look at the middle letters.
'eaten by' indicates putting letters inside (inserted letters get eaten).
'climber' becomes 'ivy' (ivy is a climbing plant).
The centre of 'pecorino' is 'or'.
'or' going into 'ivy' is 'IVORY'.
(Other definitions for ivory that I've seen before include "Smooth material of elephant tusks" , "Yellowish white - material from tusks" , "Some hunt this" , "Elephant tusk material" , "Piano-key" .)