Which book in the New Testament did St Luke write apart from the gospel which bears his name?

Answer 1

Acts of the Apostles

Answer 2

Acts of the Apostles!

Although his name isn't at the beginning, it is assumed that he wrote both books! Cf. the Gospel of Luke Chapter 1:

1 Forasmuch as many have taken in hand to set forth in order a declaration of those things which are most surely believed among us,

2 Even as they delivered them unto us, which from the beginning were eyewitnesses, and ministers of the word;

3 It seemed good to me also, having had perfect understanding of all things from the very first, to write unto thee in order, most excellent Theophilus,

4 That thou mightest know the certainty of those things, wherein thou hast been instructed.

Compare with Acts 1:

1 The former treatise have I made, O Theophilus, of all that Jesus began both to do and teach, (etc...)

Answer 3

Acts

Answer 4

Acts of the Apostles.