If the Acid is strong and Base is weak. Will there be a neutralisation reaction?
If the reaction goes to completion and all the reactants are used up, then it will be the same result as a strong acid/strong base reaction, producing a salt and water in its entirety. Because all of the strong acid will have neutralized the weak base, there will not be any of the weak base left in solution. All of it will be converted to salt. This is why titrations with weak base and strong acids are effective, because all of the weak base is reacted with the strong acid.
As with strong acid/strong base reactions, an excess of either will fully react the limiting reagent, producing a salt, water, and leaving some of the excess reagent left over. The only difference with weak acids and strong acids is that the pH of a weak acid will be closer to 7 than the pH of a strong acid of equal concentration (the same applies to strong/weak bases because they both do not fully dissociate).