Issue that's annoying bishop starts to rather amuse theologian (4)

I believe the answer is:

brat

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'issue that's annoying' is the definition.
I can't judge whether this defines the answer.

'bishop starts to rather amuse theologian' is the wordplay.
'bishop' becomes 'B' (chess abbreviation).
'starts to' indicates taking the first letters.
The first letters of 'rather amuse theologian' is 'rat'.
'b'+'rat'='BRAT'

Can you help me to learn more?

(Other definitions for brat that I've seen before include "Mervyn -- (Titus Groan)" , "Spoilt kid" , "Bad child - pack member!" , "Spoilt child" , "A spoiled badly-behaved child" .)

I've seen this clue in The Independent.

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