Hawk left after row over church (7)

I believe the answer is:

tiercel

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'hawk' is the definition.
(tiercel is a kind of hawk)

'left after row over church' is the wordplay.
'left' becomes 'l' (common abbreviation).
'after' says to put letters next to each other.
'row' becomes 'tier' (tier is a kind of row).
'over church' becomes 'ce' (abbreviation for Church of England. I am not sure about the 'over' bit.).
'tier'+'ce'='tierce'
'l' put after 'tierce' is 'TIERCEL'.

Can you help me to learn more?

(Other definitions for tiercel that I've seen before include "It flies" , "See hawk" .)

I've seen this clue in The Times.

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