Prepositional phrases such as within it have no bearing on the categorization of a clause as active or passive.
The passive is made up of the auxiliary to be and the past participle of a transitive verb. The direct object of the transitive verb becomes the subject of the passive construction.
Active: She stirred the tea with a big wooden spoon.
Passive: The tea was stirred with a big wooden spoon.
Intransitive verbs such as go, rain, happen are not followed by a direct object, and generally cannot be passivized. (But see below.)
Many verbs, however, are ambitransitive (transitive in some contexts and intransitive in others). One such verb is stir. In the tea example above, it is a transitive verb. It has a direct object and can thus be used in a passive construction.
But stir can also be used intransitively, i.e., without a direct object. Here are a few Google examples of intransitive stir:
- Her baby stirred with her.
- Something stirred within me.
- The Hulk was an ordinary person until something stirred within him.
- Nothing stirred within his soul but a cold and cruel and loveless lust.
The clause in The Hindu sentence ('a sense of India's greatness stirred within it') uses the intransitive stir and is therefore grammatical.
Intransitive verbs in passive constructions
In general terms, intransitive verbs cannot be passivized. For example:
Active: An accident happened yesterday.
Passive: * (e.g.) Yesterday was an accident happened.
But some constructions containing intransitive verbs and prepositional phrases can be passivized - with varying degrees of grammaticality.
Active: She went to the bank.
Passive: ?The bank was gone to (by her).
Active: Nobody had slept in the bed.
Passive: The bed had not been slept in.
Thanks to Janus Bahs Jacquet, who prompted this addendum.