I feel that each of these scales are not sufficient to measure construct A in a new context. But a combination of select items will help? How can we do this?
It is not problem to make combination from two scales. it is recommended to mention the scale you used. Also, when you select the variables (from two scales), and evaluate the respondents, calculate Cronbach alpha.C ronbach's alpha is a measure of internal consistency, that is, how closely related a set of items are as a group. It is considered to be a measure of scale reliability (see more about Cronbach's Alpha)
Yes, as mentioned, you may do this, particularly if the instruments are freely accessible. If you are required to pay for the measures and there are proprietary rights, you may not be able to do this (e.g., the company that owns the measure does not give you raw scores but only total scores for each participant, in this case you would not be able to combine the scales). In addition to the estimate of reliability as noted by Senad Mehmedinović (and you may wish to calculate a Cronbach alpha for the combined scales and one for each scale), you may wish to conduct some confirmatory factor analyses to determine if your data is best described by a single factor or two factors. If best described by one, then it is a good idea to combine the responses from the two scales into a total score for all other analyses or descriptive information regarding your sample. However, if responses are best described by two factors (which may be the case given that you believe they capture different aspects of your construct A), it may be best to keep them separate for subsequent analyses or when describing your samples (depending on what you want to look at or learn about your samples or your construct), you would just treat them as two separate variables that you believe describe different aspects/elements of your construct A. This does not mean you have to treat them as separate scales, it just means you could potentially lose valuable information regarding your sample or the construct if you combine them.
On a side note, I would be very careful with calculating a Cronbach's alpha for the combined scales. Bare in mind that unidimensionality is a prerequisite for Cronbach's alpha. Consequently, merely a high Cronbach's alpha for the combined scales does not allow you to join the scales.
As Adelheid Nicole mentioned, you should test if the scales measure one construct, e.g. by SEM.
We have just published an article about scale purification, i.e. the process of eliminating items from multi-item scales. Maybe our discussion can be interesting for you to consider. We have used the example of SCM, but our framework can be applied to any other discipline. Download: https://doi.org/10.1108/SCM-07-2016-0230 (or request via my ResearchGate page).