Be hard on the heels of and Run down

Run down and be hard on the heels of are semantically related. In some cases you can use "Run down" instead a verb phrase "Be hard on the heels of".

Run down verb - To come upon after searching, study, or effort.

Be hard on the heels of and run down are semantically related. Sometimes you can use "Be hard on the heels of" instead a verb "Run down".