Unseated riders, those unfamiliar with a powerful horse initially restrained (12)

'unseated riders' is the definition.
(unseated passengers on public transport)

'those unfamiliar with a powerful horse initially restrained' is the wordplay.
'those unfamiliar' becomes 'strangers' (people you don't know).
'with' is an insertion indicator.
'initially' suggests taking the first letters.
'restrained' becomes 'a' (I am not sure about this - if you are sure you should believe this answer much more).
The first letters of 'powerful horse' is 'ph'.
'ph'+'a'='pha'
'strangers' going around 'pha' is 'STRAPHANGERS'.