At heart, Balearic cassette offers calm (4)
I believe the answer is:
ease
'calm' is the definition.
(I've seen this before)
'at heart balearic cassette' is the wordplay.
'at heart' says to take the centre.
'cassette' becomes 'se' (I can't justify this - if you can you should give a lot more credence to this answer).
The middle letters of 'balearic' are 'ea'.
'ea'+'se'='EASE'
'offers' is the link.
Can you help me to learn more?
(Other definitions for ease that I've seen before include "Leisure, comfort" , "Comfort; facility" , "Move gently or carefully" , "Lack of difficulty" , "Comfort and repose" .)