School agree head's showing great enthusiasm (9)
I believe the answer is:
eagerness
'great enthusiasm' is the definition.
'school agree head's' is the wordplay.
'school' is an anagram indicator (school can mean to improve or manipulate).
'head' becomes 'ness' (ness is a headland).
'agree' is an anagram of 'eager'.
'eager'+'ness'='EAGERNESS'
'showing' acts as a link.
(Other definitions for eagerness that I've seen before include "Keenness, enthusiasm" , "'Keenness, avidness (9)'" , "Avidity" , "Keen interest" , "Sense rage (anag.)" .)