Exodus and Leviticus connect in the following ways:
Nearly the entire second half of Exodus is focused on drawing the blueprints for and constructing the tabernacle. Finally in the last chapter of Exodus the tabernacle is set up for the first time. God then fills the tent with his presence to such an extent that not even Moses could enter the tent. This is truly an amazing backdrop for the opening line of Leviticus where we are told God calls Moses into the tent. The rest of the book unfolds with "and Yahvah said" each time Yahvah spoke to Moses.
A general theme between Exodus and Leviticus is the priesthood. The actual installation of Aaron and his sons as priests happens in Leviticus 8 and following, though Exodus 28 mentions that this would eventually happen and spends detail on the production of the clothing the priests would wear on the day they would be consecrated as priests.
The priesthood story could probably be considered a sub-plot to the overall story rolling by in this section of the Bible.
More important perhaps than the installation of priests and something the installation of priests was a prerequisite for is the sacrifice linkage shared between the books of Exodus and Leviticus. Consider the reoccuring message Moses gave Pharaoh in the process of bring the Israelites out of Egypt.
He continually asked Pharaoh to let the people go so they could offer sacrifices to Yahvah in the wilderness. Of course God eventually forced Pharaoh's hand and Israel came out of Egypt, but as the rest of Exodus unfolds the attention of the book is mostly on the building of the Tabernacle and not much sacrifice happens. An inquisitive reader wonders if Moses' words to Pharaoh about sacrifice were true or perhaps only rhetoric.
Then we come to the opening chapters of Leviticus and after calling to Moses from within the newly constructed Tabernacle Yahvah says to Moses "This is how you do a sacrifice."
In fact Yahvah spends about seven chapters telling Moses how every imaginable kind of sacrifice is to be performed. So the words spoken to Pharaoh were not rhetoric, but required a Tabernacle, God's presence in the Tabernacle and the installation of priests with thier clothing and tools in hand to do a proper sacrifice. Thus the building of the Tabernacle and it's implements and the priestly clothing in Exodus connects strongly with the opening chapter of Leviticus where the sacrifices can begin with regularity.