Snag encountered involving new intake of pupils from local area (9)

I believe the answer is:
catchment
'local area' is the definition.
(as in a catchment area)
'snag encountered involving new' is the wordplay.
'snag' becomes 'catch' (I've seen this in another clue).
'encountered' becomes 'met' ('meet' can be a synonym of 'encounter').
'involving' means one lot of letters goes inside another.
'new' becomes 'n' (common abbreviation eg NT for New Testament).
'met' placed around 'n' is 'ment'.
'catch'+'ment'='CATCHMENT'
'intake of pupils from' acts as a link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for catchment that I've seen before include "collection of water" , "Area from which school's pupils are drawn" , "Area from which river derives its flow" , "collecting water" , "drainage basin" .)
