Yes, Jesus frequently quoted from and taught from what is today called the Old Testament scriptures. He regarded them as inspired and authoritative, and gave the correct interpretation as He was Himself 'the Word' made flesh.
In the example below He applied the scriptural prophecy regarding the Messiah to Himself and later on He used examples from passages to illustrate a point, although not quoting directly.
14And Jesus returned in the power of the Spirit into Galilee: and there went out a fame of him through all the region round about. 15And he taught in their synagogues, being glorified of all. 16And he came to Nazareth, where he had been brought up: and, as his custom was, he went into the synagogue on the sabbath day, and stood up for to read. 17And there was delivered unto him the book of the prophet Esaias. And when he had opened the book, he found the place where it was written, 18The Spirit of the Lord is upon me, because he hath anointed me to preach the gospel to the poor; he hath sent me to heal the brokenhearted, to preach deliverance to the captives, and recovering of sight to the blind, to set at liberty them that are bruised, 19To preach the acceptable year of the Lord. 20And he closed the book, and he gave it again to the minister, and sat down. And the eyes of all them that were in the synagogue were fastened on him. 21And he began to say unto them, This day is this scripture fulfilled in your ears. 22And all bare him witness, and wondered at the gracious words which proceeded out of his mouth. And they said, Is not this Joseph's son? 23And he said unto them, Ye will surely say unto me this proverb, Physician, heal thyself: whatsoever we have heard done in Capernaum, do also here in thy country. 24And he said, Verily I say unto you, No prophet is accepted in his own country. 25But I tell you of a truth, many widows were in Israel in the days of Elias, when the heaven was shut up three years and six months, when great famine was throughout all the land; 26But unto none of them was Elias sent, save unto Sarepta, a city of Sidon, unto a woman that was a widow. 27And many lepers were in Israel in the time of Eliseus the prophet; and none of them was cleansed, saving Naaman the Syrian. Jesus Himself was of course the central subject of what came to be called the New Testament, which had not yet been written.