Legover is slang for sexual intercourse.
Therefore, to “get one’s legover” is a blokey way of saying “to get laid”.
A famous British joke is “What do Eric Cantona and Will Carling have in common? They both got their legover at the Palace!”.
This joke refers to the Manchester United player Eric Cantona, who famously karate-kicked a fan at a match against Crystal Palace, and the rugby player Will Carling, who was rumoured to have had an affair with Princess Diana. Thus both gentlemen could be understood to have gotten their legover in a “Palace” setting!
“No matter how hard I tried, I just couldn’t get my legover!”.