In this work we study the effect of disequilibrium processes on mixing ratio profiles of neutral species and on the simulated spectra of a hot Jupiter exoplanet that orbits stars of different spectral types. We also address the impact of stellar activity that should be present to a different degree in all stars with convective envelopes. We used the VULCAN chemical kinetic code to compute number densities of species. The temperature-pressure profile of the atmosphere was computed with the HELIOS code. We also utilized the $tau$-ReX forward model to predict the spectra of planets in primary and secondary eclipses. In order to account for the stellar activity we made use of the observed solar XUV spectrum taken from Virtual Planetary Laboratory (VPL) as a proxy for an active sun-like star. We find large changes in mixing ratios of most chemical species in planets orbiting A-type stars that radiate strong XUV flux inducing a very effective photodissociation. For some species, these changes can propagate very deep into the planetary atmosphere to pressures of around 1 bar. To observe disequilibrium chemistry we favor hot Jupiters with temperatures Teq=1000 K and ultra-hot Jupiters with Teq=3000$ K that also have temperature inversion in their atmospheres. On the other hand, disequilibrium calculations predict little changes in spectra of planets with intermediate temperatures. We also show that stellar activity similar to the one of the modern Sun drives important changes in mixing ratio profiles of atmospheric species. However, these changes take place at very high atmospheric altitudes and thus do not affect predicted spectra. We estimate that the effect of disequilibrium chemistry in planets orbiting nearby bright stars could be robustly detected and studied with future missions with spectroscopic capabilities in infrared such as, e.g., JWST and ARIEL.