Individually specify setter on cryptic Times puzzle finally (7)

I believe the answer is:

itemise

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'individually specify' is the definition.
'itemise' can be an answer for 'specify' ('specify'->'itemize' is in my internal thesaurus and 'ize'->'ise'). I'm unsure of the 'individually' bit.

'setter on cryptic times puzzle finally' is the wordplay.
'setter' becomes 'i' (the person who set this crossword).
'on' says to put letters next to each other (in a down clue, letters appear on others).
'cryptic' indicates anagramming the letters (a cryptic or obscure order of the letters).
'finally' suggests the final letters.
The final letter of 'puzzle' is 'e'.
'times'+'e'='timese'
'timese' with letters rearranged gives 'temise'.
'i'+'temise'='ITEMISE'

Can you help me to learn more?

(Other definitions for itemise that I've seen before include "List in detail" , "List exhaustively" , "make inventory" , "Enumerate" , "Using spell out" .)

I've seen this clue in The Times.

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