Evidently American father, perhaps, is immersed in work (10)
I believe the answer is:
apparently
'evidently' is the definition.
(thesaurus)
'american father perhaps is immersed in work' is the wordplay.
'american' becomes 'a' (common abbreviation - e.g. in organisation names).
'father perhaps' becomes 'parent' (father is a kind of parent).
'is immersed in' indicates putting letters inside.
'work' becomes 'ply' (to ply a trade is to work at it).
'parent' put into 'ply' is 'pparently'.
'a'+'pparently'='APPARENTLY'
(Other definitions for apparently that I've seen before include "On the face of it" , "so it seems" , "Clearly" , "Seemingly" .)