Do Catholics believe in the Old Testament?
The short answer is: Absolutely!
In fact Catholic bibles include some books not found in other denominations. Canonical by the Catholic Church and the Orthodox Church (Deuterocanonical books):
Book of Tobit
Book of Judith
Book of Wisdom
Book of Baruch
Additions to Esther
Yes, Catholics must believe in the Old Testament and New Testament, and the God of the Old Testament = Holy Trinity.
The heretical Manicheans and Albigensians rejected the Old Testament. The Council of Florence's Cantate Domino (1442), promulgated by Pope Eugene IV, condemns them in part because (DZ 707):
they have said that there is one God of the New ...