To flatter, behave sycophantically (towards), or a flatterer or sycophant. A vulgarism common in all English-speaking countries at least since World War II. 'Brown-noser' is an alternative version of the noun form. From the image of kissing another person's backside. (Private Eye, the satirical magazine, has instituted a regular column in which the 'order of the Brown Nose' is awarded for nauseating sycophancy.)

brown-nosing the boss

'Now he is on his knees, brown-nosing with the rest of them.' (Private Eye, 1 April 1988).