Teacher with complaint or problem after retiring (6)

I believe the answer is:

bedbug

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'problem after retiring' is the definition.
I can't tell whether this definition defines the answer.

'teacher with complaint' is the wordplay.
'teacher' becomes 'BEd' (holder of a BEd, Bachelor of Education degree).
'with' is a charade indicator (letters next to each other).
'complaint' becomes 'bug' (medical complaint).
'bed'+'bug'='BEDBUG'

'or' is the link.

Can you help me to learn more?

(Other definitions for bedbug that I've seen before include "It sucks your blood while you sleep" , "Bloodsucker's" , "Sleeper biter?" , "Night-time pest" , "Night-time biter" .)

I've seen this clue in The Times.

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