You can have it.

ageru : give

conjugation
age-nai : give not
age-masu : give (polite)
ageru : give (plain)
ageru -toki : give when
ager-eba : give if
ager-o : give(imperative)

ageru darou : will give
ageta : gave

anata : you
ni :to
kore : this

Anata ni kore o agemasu. : (the subject "watashi wa" omitted) ,you to, this, give.: I give you this.

When the recipient is "me", "kureru" should be used in spite of "ageru".

Anata wa watashi ni kore o kuremasu. : you, me to, this, give.: You give me this.

kare : he , his, him
kanojo : she, her, her

Kare wa kanojo ni kore o ageta. : he, her to, this, gave : He gave her this.
Anata wa kare ni kore o ageta. : you , him to, this, gave : You gave him this.
Kare wa watashi ni kore o kureta. : he, me to, this, gave : He gave me this.

kureru : give

conjugation
kure-nai : give not
kure-masu : give (polite)
kureru : give (plain)
kureru-toki : give when
kurer-eba : give if
kure : give (imperative)

kureru darou : will give
kureta : gave

Kore o kanojo ni agero : this, her to, give(imperative).:Give her this.
Kore o watashi ni kure : this, me to, give. : Give me this.

When the recipient and "me"(the first person) is in the same group like family, "kureru" can be used.

omocha : toy
musuko : son
watashi no : my

Kare wa watashi no musuko ni omocha o kureta. : he, my son to, toy,gave : He gave a toy to my son.

We can say that "ageru" has a nuance of "going out", "kureru" has "coming in".