People in authority briefly entertaining computing tax (5)
I believe the answer is:
tithe
'tax' is the definition.
(I've seen this before)
'people in authority briefly entertaining computing' is the wordplay.
'people in authority' becomes 'they' (I've seen this in other clues).
'briefly' means to remove the last letter.
'entertaining' indicates putting letters inside.
'computing' becomes 'it' (IT is an abbreviation for Information Technology).
'they' with its final letter removed is 'the'.
'the' enclosing 'it' is 'TITHE'.
(Other definitions for tithe that I've seen before include "Former church tax" , "donation to church" , "10 per cent levy" , "Gift of tenth" , "Tenth (of one's earnings)" .)