The finest possibly head master: that’s obvious (8)
I believe the answer is:
manifest
'obvious' is the definition.
(similar in meaning)
'the finest possibly head master' is the wordplay.
I cannot quite see how this works, but
'the' could be 't' (the is pronounced as a 't' sound in some dialects) and 't' is located in the answer.
'master' could be 'ma' (Master of Arts) and 'ma' is found in the answer.
This explanation may well be incorrect...
'that's' is the link.
Can you help me to learn more?
(Other definitions for manifest that I've seen before include "Ship's document; plain" , "List of ship's cargo or passengers" , "Display" , "Document listing a ship's contents for customs purposes" , "Conspicuous; cargo list" .)