Typically, for most projects, the decision on the outcome of a planning application is made within eight weeks. For very large or complicated developments, this can be extended to thirteen weeks, after gaining your written consent. It is likely that the LPA will be able to give you a timeframe.
If the LPA does not seek your written consent to extend the period, then you can appeal to the secretary of state. Do be aware, however, that this can take months, so it may be faster to contact the LPA and reach an agreement if time is of the essence.