It's a bit unusual (why don't you want to estimate the trend for the new time series?), but if you are really interested in I can recommend to estimate the residuals after the implementation of initial time series' trend to another one. And if your residuals have no any other tendencies (you could check it with some methods like Mann-Kendall test, or Foster-Stuart test, or many others), you will be assured that you can apply your trend to the new data properly.

There are methods for testing whether data in a time series deviates significantly from that predicted by a model fitted previously  to another time series. These are used in industrial quality control and in clinical monotoring. see eg Armitage and Berry Statistical Methods in Medical Research,  Blackwell 2nd ed 1987 p 347-352.

It's a bit unusual (why don't you want to estimate the trend for the new time series?), but if you are really interested in I can recommend to estimate the residuals after the implementation of initial time series' trend to another one. And if your residuals have no any other tendencies (you could check it with some methods like Mann-Kendall test, or Foster-Stuart test, or many others), you will be assured that you can apply your trend to the new data properly.

Take a look at this paper

https://www.researchgate.net/publication/268204916_Dynamic_Pattern_Matching_Using_Temporal_Data_Mining_for_Demand_Forecasting

Article Dynamic Pattern Matching Using Temporal Data Mining for Dema...