Efficiency can be increased by using line feed technique in stead of coaxial probe. As return loss,Gain and radiation pattern are important similarly efficiency is very important parameter for analysing MSA.
Find out the point where the impedance excatly match as that of the characteristic impedance of ur feed line for cozxial feed.. If inset feed we use to make use the radiating structure effectively which improves efficiency..
First you have to eliminate bad matching in input, that means using impedance transformers or BALUN network. But if you have the perfectly matched antenna, still there would not be perfect radiation; because the antenna structure determines how the current would distribute on antenna. And when the current is not distributed to radiate, the radiation efficiency degraded.
One traditional way is to increase dielectric constant but in this way the antenna performance become narrow-band.
The other way is to observe the current distribution on antenna structure and try to reshape its structure so maximum current get closer to its edge. This again might result in bandwidth degradation.
You may follow designing method concerning with impedance matching if required use BALUN Network. Again you have to look for efficiency types which one you want to improve overall antenna efficiency or only radiation efficiency. If concern is antenna efficiency then material losses (copper or dielectric losses) are an important factor.
You can apply reflecting surfaces, active component, EBG structure or slot matching etc to improve radiation efficiency.
You can follow my latest method on same topic a novel approach
Salamin, M.A., Ali, W.A.E., Das, S. et al. A novel etched-substrate mechanism for characteristics improvement of X-band broadband printed monopole antenna. Microsyst Technol (2020). https://doi.org/10.1007/s00542-020-04862-1