Put down cellist’s first record (4)
I believe the answer is:
disc
'record' is the definition.
(synonyms)
'put down cellist's first' is the wordplay.
'put down' becomes 'dis' (I can't explain this - if you can you should give a lot more credence to this answer).
'cellist's first' becomes 'c' (dst letter of 'cellist').
'dis'+'c'='DISC'
Can you help me to learn more?
(Other definitions for disc that I've seen before include "Layer of cartilage between spinal vertebrae" , "something moving in the spine" , "Sound recording" , "Body without limbs" , "In Olympic event" .)