You describe someone as a social climber when they try to get accepted into a higher social class by becoming friendly with people who belong to that class.
[disapproval]
That he was a snob and a social climber could scarcely be denied.
social climber in British English
noun
a person who seeks advancement to a higher social class, esp by obsequious behaviour
Sometimes shortened to: climber
Derived forms
social climbing
noun
social climber in American English
US
a person who associates with socially prominent people in an attempt to gain higher social status
Examples of 'social climber' in a sentence
social climber
I gather your father is bankrupt and your mother a contemptible social climber.
Diana Wynne Jones THE LIVES OF CHRISTOPHER CHANT (1988)
social climber