The 21-year-old model shared a similar post, which showed the couple in a close – and cheeky – embrace.
The pair also shared a series of Instagram Stories as they walked along a beach.
The couple confirmed their romance last week, pictured holding hands as they left the British Fashion Awards party.
It seems the 19-year-old is well a truly moved on from his relationship with actor Chloë Grace Moretz, who he dated on and off for four years before ending things in April 2018.
No word on how the new couple met, however Cross is a fellow Brit who appears to be a close friend of his cousin Libby Adams.