The word covenant is used in different accounts in the Holy Qur'an to describe many kinds of relationships and agreements.
In many verses for example, we read about God's ancient covenant with mankind, that in return for God's protection, favors and guidance, we need to abide by His laws, live according to His commandments and accept and obey His Messengers.
God's Covenant with Mankind:
"And when We made a covenant with the children of Israel: You shall not serve any but Allah and (you shall do) good to (your) parents, and to the near of kin and to the orphans and the needy, and you shall speak to men good words and keep up prayer and pay the poor-rate. Then you turned back except a few of you and (now too) you turn aside."
"It is not piety, that you turn your faces to the East and to the West. True piety is this: to believe in God, and the Last Day ... to give of one's substance ... and to ransom the slave, to perform the prayer, to pay the alms. And they who fulfill their covenant ... and endure with fortitude."
"..., but He causes not to stray, except those who forsake (the path),- Those who break Allah's Covenant after it is ratified, and who sunder what Allah Has ordered to be joined, and do mischief on earth: These cause loss (only) to themselves."
Part of this covenant is to accept God's Messengers:
Certainly We made a covenant with the children of Israel and We sent to them apostles; whenever there came to them an apostle with what that their souls did not desire, some (of them) did they call liars and some they slew.
"O children of Adam! When Messengers come to you from among you, who convey my verses, then those who take heed and amend will have neither fear nor regret."
Another translation of this verse (by Yusuf Ali) is:
O ye Children of Adam! whenever there come to you messengers from amongst you, rehearsing My signs unto you,- those who are righteous and mend (their lives),- on them shall be no fear nor shall they grieve.