Yes, we can have an accelerated body with constant speed as we see in uniform circular motion. Acceleration is co-related with velocity as it is the change in velocity per unit time and that velocity is a vector quantity ,therefore,its is related with direction .                                                                              For eg. in the uniform circulatory motion the velocity of the body changes at every point as the direction changes and that is why it is said to be accelerated  whereas speed does not depend on direction ,so , we can have a body accelerated and moving with a constant speed at the same point of time.                                                                  I HOPE IT HELPED U :)                                                                   Please rate so that I could check where I stand