A source tells PEOPLE that Don Jr. is "smitten" with Anderson and claims that he began introducing her as his girlfriend months ago

It’s out with the old and in with the new as Donald Trump Jr. steps out with Palm Beach socialite and model Bettina Anderson while his ex-fiancée Kimberly Guilfoyle packs her bags for Greece. The president-elect’s son has been repeatedly pictured alongside Anderson in recent months and the pair was caught locking lips in August,

The socialite was spotted sitting behind Trump and Guilfoyle at the Republican National Convention in Milwaukee, Wis., in mid-July. Anderson was also photographed chatting with Don Jr.’s ex, Vanessa Trump, 46, at the event, and we’d heard that the two are close friends, and that Anderson attended the convention with Vanessa.