Rustic husband deserts bird (7)

I believe the answer is:

peasant

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'rustic' is the definition.
(I know that peasant is a type of rustic)

'husband deserts bird' is the wordplay.
'husband deserts' becomes 'peas' (I am not sure about this - if you are sure you should believe this answer much more).
'bird' becomes 'ant bird' (ant bird is a kind of bird).
'peas'+'ant'='PEASANT'

Can you help me to learn more?

(Other definitions for peasant that I've seen before include "rude fellow" , "Rural person of low class" , "Provincial" , "Rural labourer" , "Poor smallholder" .)

I've seen this clue in The Sun.

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