1
general::
Try to impress or please, be attentive to, as in George was always shining up to the teacher, or Her father warned her about men shining up to her for her money. [Colloquial; late 1800s]
American Heritage Idioms
2
general::
Phrase(s): shine up to someone
Fig. to try to gain someone’s favor by being extra nice. • John is a nice guy, except that he’s always trying to shine up to the professor. • Mary never tries to shine up to the manager.
McGrawhill's American Idioms And Phrasal Verbs