Verbs

(v)intercede, mediate, intermediate, liaise, arbitrateact between parties with a view to reconciling differences“He interceded in the family dispute”, “He mediated a settlement”
(v)mediateoccupy an intermediate or middle position or form a connecting link or stage between two others“mediate between the old and the new”

Adjectives

(a)mediateacting through or dependent on an intervening agency“the disease spread by mediate as well as direct contact”
(s)in-between, mediate, middlebeing neither at the beginning nor at the end in a series“adolescence is an awkward in-between age”, “in a mediate position”, “the middle point on a line”