Step 1: Understand stereogenic centres.
A stereogenic centre is usually an sp$^3$ carbon atom attached to four different groupsChanging the configuration at such a centre gives a stereoisomer
Step 2: Examine the alkaloid structure.
The given alkaloid contains a quinoline ring system and a bicyclic amine portionThe aromatic carbons are sp$^2$ hybridized and cannot act as stereogenic centres
Step 3: Locate stereogenic centres in the side chain.
The carbon bearing the hydroxyl group is attached to four different groupsTherefore, it is one stereogenic centre
Step 4: Locate stereogenic centres in the bicyclic amine part.
The bicyclic quinuclidine-type portion contains multiple asymmetric sp$^3$ bridgehead/substituted carbonsThese carbons are attached to different paths in the ring system and hence act as stereogenic centres
Step 5: Count valid stereogenic centres.
On careful inspection, four sp$^3$ carbons satisfy the condition of being attached to four different groups
Step 6: Exclude non-stereogenic atoms.
The nitrogen atom is not counted because rapid inversion at nitrogen generally prevents stable configurational chiralityThe alkene and aromatic carbons are also not counted because they are sp$^2$ hybridized
Step 7: Conclusion.
Thus, the number of stereogenic centres present in the given alkaloid is
\[
\boxed{4}
\]