To foretell - accurately.
A regular verb.
Just as remember is in the past - after an event looking back, so premember is something you do before an event, looking ahead.
Just as the French have a phrase 'deja vu' we English use premember; so - "Shall we premember the score of tonight's big match?"
"There he sits, premembering his order at the chip shop."
"Yeah, and I'll have a large cod with vinegar, no salt; d'you reckon he'll premember that?"