Lag time, an annoyance (6)

I believe the answer is:

inmate

I'm a little stuck... Click here to teach me more about this clue!

'lag' is the definition.
(I've seen this before)

'time an annoyance' is the wordplay.
'time an' can be anagrammed to 'INMATE'.
Though, I'm not sure how the anagram is indicated.

Can you help me to learn more?

(Other definitions for inmate that I've seen before include "One institutionally confined" , "Convict" , "Someone confined, eg to hospital or prison" , "Occupant" , "Inhabitant of prison or hospital" .)

I've seen this clue in the Sydney Morning Herald.

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