The prediction for 2015-2016
The LHC will collect about 10 inverse femtobarns of proton-proton collisions data this year. ATLAS and CMS will work perfectly well - as they have in the past. Summer conferences, however, will not offer new discoveries, as the data samples used for the presented analyses will be small. The focus there will be the "re-discovery" of the Higgs boson and some more detailed fits of its properties. No departures will be seen from Standard Model predictions there. No new gauge bosons - the Z' in particular - will be reported either: the dimuon and dielectron mass distributions will exhibit nicely falling spectra with no bump at the high end, as they always have and always will (recall that one of the new physics processes which would benefit the most from the 60% increase in center-of-mass of the collisions is the quark-antiquark production of a Z' boson, hence it would be one of the first things the LHC could discover - if there were a Z').
Then, at the first winter conferences in early 2016 ATLAS and CMS will both report new results based on the full 2015 datasets. And nobody will pay much attention to the Higgs anymore, as the two experiments will both present some mild excess of events with large missing transverse energy and multiple hadronic jets. Taken independently the two results will not appear exciting, standing at less than three standard deviations above backgrounds; yet everybody will at once notice that they confirm one another, and together they add up to a four standard deviations effect.
A Supersymmetric gluino signal will immediately appear as a plausible explanation for the observed phenomena, and theorists will go in a state of feeding frenzy, resurrecting the MSSM in its various declinations in an attempt to fit as well as possible the CMS and ATLAS data, together with the more precise information on the Higgs boson and other exclusion limits in dedicated SUSY searches. About 200 papers will be published which cite the new LHC results in the matter of three months.
The restart of the LHC will be a giant triumph for CERN, as the expectation for the new data will be at a record high, surpassing that for the Higgs of the spring of 2012. And the experiments will not wait for the fourth of July to make an announcement this time, as the first two months of the anticipated 2016 running of the accelerator will already yield a doubling of the 13 TeV data, and a discovery of new physics will be announced in early June.
This, dear reader, is what I would like to happen, despite my general disbelief of Supersymmetric theories, and despite the new $1000 bet I have offered against such new signals in LHC data in the coming years (nobody has taken the new bet, unfortunately). A supersymmetric world would be an amazing thing to investigate, and a much more interesting one than the one we seem to live in.