The opposite ${\mathrm{ℬ︀}}^{\text{op}}$ of a bicategory $\mathrm{ℬ︀}$ has the same 0-cells and reverses the 1-cells but not the 2-cells:

Composition swaps its arguments, $𝑓{\star }^{\text{op}}𝑔=𝑔\star 𝑓$. The left unitor of ${\mathrm{ℬ︀}}^{\text{op}}$ is the right unitor of $\mathrm{ℬ︀}$ and vice versa, and the associator of ${\mathrm{ℬ︀}}^{\text{op}}$ is the inverse of the associator of $\mathrm{ℬ︀}$, with its arguments reversed.

Since the 2-cells keep their direction, a lax functor $𝐹:\mathrm{ℬ︀}\to \mathrm{𝒞︀}$ induces a lax (not oplax) functor ${\mathrm{ℬ︀}}^{\text{op}}\to {\mathrm{𝒞︀}}^{\text{op}}$ with the same action on cells. Reversing the 2-cells instead gives the bicategory ${\mathrm{ℬ︀}}^{\text{co}}$, whose hom-categories are the opposites ${(\mathrm{ℬ︀}(𝑥,𝑦))}^{\text{op}}$.

Duality saves work: a coherence lemma about $\mathrm{ℬ︀}$ can often be obtained by instantiating a companion lemma at ${\mathrm{ℬ︀}}^{\text{op}}$, which swaps left and right.