The fulfillment of time that Jesus is referring to is the completion of the time of the Law, and the beginning of the time of the Gospel.
Paul wrote to the Galatians (4:4) that
when the fullness of the time came, God sent forth His Son, born of a woman, born under the Law, so that He might redeem those who were under the Law
According to what he wrote the Ephesians (1:10), this redemption of those under the law was existential and not merely judicial:
In the dispensation of the fullness of times, He might recapitulate all things in Christ, both which are in heaven, and which are on earth, in Him
I know of no translation other than The Orthodox New Testament (and a translation of a Greek commentary on Ephesians 1:10) that choose to translate ἀνακεφαλαιώσασθαι as "recapitulate", but that is closer to the literal meaning - κεφαλαιώσασθαι is an extremely rare verb related to κεφαλή (head), with the prefix ἀνα- equivalent to our English "re-" in this context. The sense is to gather (back) all things under Christ as the head.
After telling that the time is fulfilled, the very next thing Jesus does is not only to call the hearer to repentance, but to believe the gospel. We think of repentance in terms of regret or sorrow, but this is not really what the Greek μετάνοια means. It too reflects an existential and not a juridical change: the root of μετάνοια is νοῦς, which is sometimes translated as "mind", but which would later be described as one's spiritual core.
So to "recapitulate", I would say the "fulfillment of time" here corresponds directly to what Paul explains in Galatians and Ephesians: an ending of the time of the Law, and a gathering of all under Christ as their head. The accompanying call to repentance should not, I think, be understood as a chastisement, but rather as an invitation.
One Greek commentator explained Mark 1:14-15 as follows:
It may appear that the Lord is preaching the same things as John, "Repent" and "The kingdom of God is at hand." But it is not so. For John said, "Repent", meaning "Turn away from sins." But Christ says, "Repent," meaning "flee from the letter of the law." This is why He also added the words, "Believe in the Gospel, the Good Tidings." For he who is about to believe through the Gospel, has in fact finished the law. The Lord says that the very time of the law has been fulfilled. Up until now, He says, the law governed, but form now on there is the kingdom and rule of God, that is, a life governed by the Gospel, and such a life is rightly compared to the kingdom of heaven.*
* Theophylact of Ohrid (11th c. Byzantine), The Explanation of the Holy Gospel According to Mark (tr. from Greek, Chrysostom Press, 1993), p.17