I don't think you can make a such a statement.
As a simplification let's assume that there is only one bond eligible for delivery into the futures (hence the CTD does not change, and the short's switch option value is 0).
- Carry of a long basis trade (i.e., long cash bond and short futures now, deliver bond into the futures at delivery) is decomposed into
$$
\text{Carry} = \text{Interest income} - \text{Financing/Repo cost}
$$
which, in an absence of arbitrage, is equal to the basis of the bond (since there is no delivery option value):
$$
\text{Carry} = \text{Bond basis} = \text{Bond clean price} - \text{Futures price} \times \text{conversion factor}.
$$
- Implied repo rate (IRR) is the return of this long basis trade, excluding financing cost, i.e.,
$$
\text{IRR} = \frac{\text{Invoice price} - \text{Purchase price}}{\text{Purchase price}} \times \frac{360}{n},
$$
where $n$ is the length of the trade in days, and the invoice price is the price you would receive when delivering the cash bond into the futures:
$$
\text{Invoice price} = \text{Futures price}\times \text{conversion factor} + \text{Bond interest accrual at delivery}.
$$
and Purchase price is the price you pay for the bond now:
$$
\text{Purchase price} = \text{Bond clean price} + \text{Interest accrual now}.
$$
As you can see carry is a dollar amount of the trade, while IRR is a rate, therefore you cannot get one from another by simple addition/subtraction.
In fact, if you play with the two relations above, you should arrive at
$$
\text{IRR} = \frac{\text{Interest income}-\text{Carry}}{\text{Purchase price}} \times \frac{360}{n},
$$
which is equal to the financing/repo rate absent of arbitrage (as the name IRR implies).
Both Carry and IRR are affected by the bond price, and in turn, its yield. But there is no simple relationship of the kind you suggested.
Edit:
If carry is defined as a rate:
$$
\frac{\text{Interest Income} - \text{Financing/Repo cost}}{\text{Purchase price}} \times \frac{360}{n},
$$
and "yield" refers to the rate at which interest is earned, as a percentage of dirty price (note that this is different from YTM or current yield as conventionally defined):
$$
``\text{yield''} = \frac{\text{Interest Income}}{\text{Purchase price}} \times \frac{360}{n},
$$
then indeed we have
$$\text{carry} = ``\text{yield"} - \text{financing/repo rate}.$$
But I don't think I have seem "yield" defined in this way.
Like many others I would recommend The Treasury Bond Basis for understanding the treasury futures products.
