organ
bone-marrow, heart, kidney, liver, lung, stem-cell, etc.

need, require
wait for
patients waiting for heart transplants

get (informal), have, receive, undergo
She will have to have a kidney transplant within 48 hours.

carry out (esp. BrE), do, perform
reject
It is likely that such a transplant will be rejected in older people.

operation, surgery
surgeon
team
centre/center, unit (esp. BrE)
donor
A suitable transplant donor has been found.

candidate, patient, recipient

for transplant
a shortage of kidneys for transplant

successfully

from, into
Organs are transplanted from donors into patients who need them.

to
The Dutch successfully transplanted trees to the East Indies.

Transplant is used with these nouns as the object:
organ