4U 1822 - 37 is a Low Mass X-ray Binary ( LMXB ) system with an Accretion Disk Corona . It is one of the very few LMXBs that shows narrow X-ray eclipses and small amplitude pulsations of the neutron star . The X-ray eclipse is an excellent reference for measurement of orbital evolution of the binary , and we have obtained 16 new mid-eclipse time measurements of this source during the last 13 years using X-ray observations made with the RXTE -PCA , RXTE -ASM , Swift -XRT , XMM-Newton and Chandra observatories . These , along with the earlier known mid-eclipse times have been used to accurately determine the timescale for a change in the orbital period of 4U 1822 - 37 . We have derived an orbital period P _ { orb } = 0.23210887 ( 15 ) d , which is changing at the rate of \dot { P } _ { orb } = 1.3 ( 3 ) \times 10 ^ { -10 } d d ^ { -1 } ( at T _ { 0 } = MJD 45614 ) . The timescale for a change in the orbital period is P _ { orb } / \dot { P } _ { orb } of 4.9 ( 1.1 ) \times 10 ^ { 6 } yr. We also report the detection of 0.59290132 ( 11 ) s ( at T _ { 0 } = MJD 51975 ) X-ray pulsations from the source with a long term average \dot { P } _ { spin } of -2.481 ( 4 ) \times 10 ^ { -12 } s s ^ { -1 } , i.e. , a spin-up time scale ( P _ { spin } / \dot { P } _ { spin } ) of 7578 ( 13 ) yr . In view of these results , we have discussed various mechanisms that could be responsible for the orbital evolution in this system . Assuming the extreme case of conservative mass transfer , we have found that the measured \dot { P } _ { orb } requires a large mass transfer rate of ( 4.2 - 5.2 ) \times 10 ^ { -8 } M _ { \odot } yr ^ { -1 } which together with the spin up rate implies a magnetic field strength in the range of ( 1 - 3 ) \times 10 ^ { 8 } G. Using the long term RXTE -ASM light curve , we have found that the X-ray intensity of the source has decreased over the last 13 years by \sim 40 \% and there are long term fluctuations at time scales of about a year . In addition to the long term intensity variation , we have also observed significant variation in the intensity during the eclipse . Variation was also seen in the pulse profile , which could be due to changes in the accretion geometry . We briefly discuss the implications of these results on our understanding of the properties of the neutron star and the accretion geometry in this source .