In this/that connection
Definition 1 of 1
Pro Tip 1/3Contextual Relevance
Use it to link relevant facts or arguments to what's being discussed. 
Regarding the budget cuts, I have some concerns in this connection.
Pro Tip 2/3Sense of Continuity
It's good for continuing a train of thought, especially after a pause or new topic. 
Let's resume our meeting — in that connection, the marketing strategy needs revising.
Pro Tip 3/3Clarification Cues
Signal that you're providing more info or explanation on the previous topic. 
About the new policy changes – I'd like to add something in that connection.