Some American people’s unfamiliar, clumsy, and I would add welcome customs (15)

'some american people's' is the definition.
(people from New Hampshire)

'would add welcome customs' is the wordplay.
'would' becomes 'newham' (I can't justify this - if you can you should give a lot more credence to this answer).
'add' becomes 'ps'.
'welcome' becomes 'hi' (I've seen this in other clues).
'customs' becomes 'rites' (both can mean rituals or traditions).
'newham'+'ps'+'hi'+'rites'='NEWHAMPSHIRITES'

'unfamiliar clumsy and i' is the link.
This may not be right. Some or all of it may belong to another bit of the clue.