move on

verb

To continue; to proceed; to go on.
“After spending the night resting in an abandoned church, the group decided to move on in their quest.”
“Moving on again, I catch another GWR Class 802 bound for Oxford via the Cotswold Line.”
To start dealing with something else.
“I could never be what she wants of me (won't you tell her?), hey / I'll just pass her by, I don't want to make her cry (won't you tell her?) hey / (Hope she finds a happy home, I think it's best that I move on, hey (hey) / I could never be what she wants of me, hey”
“The best revenge is always to just happily move on and let karma do the rest.”
To attempt a seduction, often in a way seen as disloyal or rude to another.
“I think Shane is going to move on my ex tonight.”
To physically move something or someone.
“The police moved the protestors on.”
“"When it was all British Rail, if they had some redundant sidings, they would dump all their old trains. There wasn't really a pressure to get rid of them. Now, with private companies owning the sites, you have to pay to store vehicles. Nobody wants old vehicles sat around - they can be graffitied, vandalised - and so the onus really is to move them on.”
To assault or attack.