Deuteronomy 4:13
And he declared unto you his covenant, which he commanded you to perform, even ten commandments; and he wrote them upon two tables of stone.
Deuteronomy 9:9-11
When I was gone up into the mount to receive the tables of stone, even the tables of the covenant which the LORD made with you.
Indeed,
"His covenant" (Deuteronomy 4:13) and God's
"my covenant" (Exodus 19:5) is
not ever the 'old covenant' in all of scripture. The 'old covenant' is identified clearly in Hebrews 9:6-9, which points to Exodus 19:8,
"All that the LORD hath spoken we will do.".
God came with terms,
"If ...",
"... then ..."
The people agreed (Exodus 19:8).
Covenant (old) struck between God and man, with Mediator Moses.
Yet when God spake the Ten Commandments aloud, it was directly, and no Mediator.
There are 2 (two) covenants in Exodus 19.
[1] God's covenant ("His covenant", and "my covenant") - the Ten Commandments (which is eternal, everlasting) (Exodus 19:5), and this existed between the Father and Son in eternity.
Psa_89:34
My covenant will I
not break,
nor alter the thing
that is gone out of my lips.
[2] the 'old covenant', which is the
agreement between God and the people through their promises, (Exodus 19:8 (also Exodus 24); Hebrews 8:6-9, "fault", "promises", "them")
Again, you are eisegetically reading into Deuteronomy 4:13 and Deuteronomy 9:9-11 your own personal definition when you read "covenant".
The Ten Commandments, the Law of God, His Covenant,
cannot be and are
never called in scripture, the 'old covenant', see Romans 3:31; Jeremiah 31:33 (cited in Hebrews 8).