You should specify which type of silver you want to measure.
If you wish to measure total silver (soluble + insoluble) you can performe nitric acid digestion and atomic absorption spectrometry.
If you want to measure soluble silver, you should first ultracentrifuge the solution to sediment the insoluble silver particles. Then use supernatant to measure silver as mentioned above.
Subtract soluble silver from total silver to attain insoluble silver.
If you want to determine silver as ppm scale, you can use all atomic absorption spoctrometry methods.
Seyyed Morteza Hoseini gave a good answer. I just have one addition: you can use a Ag ion selective electrode to measure the ionic Ag content, as an alternative to the ultracentrifuge method. Also, if you digest you solution, carefully check the recovery of silver during the digestion, so you don't loose any silver along the way.
The nanoparticles suspension should digested to with equal of 70 % HNO3 and heated. The silver content will be measured by atomic absorption spectrometry (AAS) or atomic absorption spectrometry graphite furnace (GFAAS).