Same way you would any other conquered world - with a lot of troops and terror.
The Betazeds, if I recall correctly, could communicate telepathically, but couldn't control minds or anything like that.
Maybe it's a prejudice, but the Betazoids don't strike me as the most asskicking people in the Federation.
Then again, the British and, to a lesser degree, French Empires, arguably among the most warlike players in the 1930s, maintained largely obsolete defenses and offenses (the navies excluded) right until the start of WWII.
I wasn't aware that there was a "problem", though...?
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