Im the sentence, the pen you gave her in the morning is lost"you gave her in the morning is an_?

"you gave her in the morning" is an adjective clause.

It modifies or specifies which pen.

Explanation: If the word "that" had been included, as in

"that you gave her in the morning"  it would be a relative clause; 'that' is a relative pronoun.

(In your question the "an___" is a hint that the answer starts with a vowel)

In any case, they are clauses, not phrases, because they include a subject, 'you', and a predicate, 'gave her in the morning.'

put the trash into the back of the truck and drive the truck to the back. then you must unload the truck.

elon musk, ceo of spacex, a startup space company is planning to head to mars by 2023. nasa is planning to go to mars at around 2025. both are just for a basic colony.