ballpoint, feather (AmE), felt, felt-tip, felt-tipped, fountain, gel, highlighter (esp. BrE), ink, marker (esp. BrE), marking (AmE), quill
calligraphy
coloured/colored
digital

use, write (sth) with
grab (esp. AmE)
I grabbed a pen and began taking notes.
Let me grab a pen.

cap, uncap
tap, twirl
borrow
Can I borrow your pen?

wield (figurative)
The President has yet to wield his veto pen to block a bill. (AmE)

write
This pen won't write.

run out
My pen's run out (= has no more ink).

be poised
His pen was poised, ready to sign his name.

nib
cap
ink (esp. AmE)
holder
mark
drawing
portrait (= written description of sb)

pen and ink
pen-and-ink drawings

Pen is used with these nouns as the object:
article, autobiography, lyrics