Yes, CLIMBERS is a Scrabble word!

Letter values in Scrabble US: C 3, L 1, I 1, M 3, B 3, E 1, R 1, S 1.

Is it a valid word?

CLIMBERS is a valid word in the official Scrabble dictionary (US), the UK Scrabble Dictionary and Words with Friends (ENABLE).

a vine or climbing plant that readily grows up a support or over other plants
someone seeking social prominence by obsequious behavior
someone who ascends on foot
someone who climbs as a sport; especially someone who climbs mountains
an iron spike attached to the shoe to prevent slipping on ice when walking or climbing

Also: social climber, climbing iron.