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"dull thy palm"
Context and Language Videos
Act 1,
Scene 3
Lines 62-68

A discussion of  "dull thy palm" in Act 1, Scene 3 of myShakespeare's Hamlet. 

Polonius 

Those friends thou hast, and their adoption tried,
Grapple them to thy soul with hoops of steel,
But do not dull thy palm with entertainment
Of each new-hatched, unfledged comrade. Beware 
Of entrance to a quarrel, but being in, 
Bear't that the opposèd may beware of thee. 
Give every man thy ear, but few thy voice.
Video Transcript: 

POLONIUS: But do not dull thy palm with entertainment Of each new hatch'd, unfledged comrade.

RALPH: So in other words, don't waste your time meeting and befriending every young guy around.

SARAH: The image here is that of making the palms of your hands calloused from shaking hands so much. Also, unfledged refers to a fledgling, a young bird which has not yet developed its feathers. So Polonius is comparing inexperienced young men to fledglings that are not yet able to fly.