@WBYeats,
@YBYeats the word "Strive" is an intransitive verb meaning "try hard to achieve something".
For the object/noun/pronoun the preposition that is always used is "for". So the above mentioned sentence is not correct.
The correct one:
We encourage all members to strive for the highest standards.
"Strive" when used as an infinitive will be dealt just as a nomal.
So "strive for something" or "strive to do something".
As fas as the verb "Aspire" is concerned, it has a slight different meaning.
Strive = Try hard to get.
Aspire = Having a desire (in heart) to get.
i.e. Aspire has nothing to do with "try" where as strive has a lot.
OR
The one who aspires to (do) something may not be trying to achieve it as it is a mere desire (no matter how strong it may be). While the one who strives is already TRYING HARD.
hope that answers.